Generalized Additive Models with Neural Networks extend the classic GAM framework by replacing spline-based shape functions with neural network sub-models — each $f_i(x_i)$ is a neural network that learns arbitrarily complex univariate transformations while maintaining the additive (interpretable) structure.

GAM-NN Architecture

• Classic GAM: $g(mu) = eta_0 + f_1(x_1) + f_2(x_2) + ldots$ where $f_i$ are smooth splines.
• Neural GAM: Replace splines with neural networks — more flexible but still additive.
• Interaction Terms: Can add pairwise interaction networks $f_{ij}(x_i, x_j)$ for controlled interaction modeling (GA$^2$M).
• Link Function: Supports any link function (identity, logit, log) for different response types.

Why It Matters

• Best of Both Worlds: Neural network flexibility with GAM interpretability.
• Pairwise Interactions: GA$^2$M adds interpretable pairwise interactions while remaining interpretable.
• Healthcare/Finance: Adopted in domains requiring model interpretability by regulation (FDA, banking).

Neural GAMs are flexible yet transparent — using neural networks within the additive model framework for interpretable, regulation-friendly predictions.